The 30-year-old took 10 wickets in the opening match of the Ashes, including the decisive one of Brad Haddin, as the Three Lions earned a 14-run victory over the travellers at Trent Bridge to take a 1-0 lead in the series.
"Australia hold Anderson in so much higher regard than the rest of the attack," Gilchrist told BBC Sport. "They are very, very wary of him and concerned about how consistent he is in any conditions.
"Brad Haddin took a strong attack to Steven Finn and even Graeme Swann, who was off his game to an extent.
"That huge feeling of reliance on Anderson, maybe they can use that to their advantage when coming up against the other bowlers."
The second Test gets underway at Lord's on Thursday.